Answer:
α = 0.22°
Step-by-step explanation:
To find the angle between the two refracted beams we need to use Snell's Law:
[tex] n_{1}sin(\alpha_{1}) = n_{2}sin(\alpha_{2}) [/tex]
Where:
n₁: is the refractive index of the incident beam (air) = 1
n₂: is the refractive index of the refractive beam (glass)
α₁: is the angle of the incident beam = 60°
α₂: is the angle of the refractive beam
Hence, for the beam with λ = 450 nm and n₂ = 1.4820, the refractive angle (α₂) is:
[tex] sin(\alpha_{2}) = \frac{n_{1}}{n_{2}}*sin(\alpha_{1}) = \frac{1}{1.4820}sin(60) = 0.5844 [/tex]
[tex] \alpha_{2} = 35.76 ^{\circ} [/tex]
Similarly, the refractive angle for the beam with λ = 700 nm and n₂ = 1.4742 is:
[tex] sin(\alpha_{2}) = \frac{n_{1}}{n_{2}}*sin(\alpha_{1}) = \frac{1}{1.4742}sin(60) = 0.5875 [/tex]
[tex] \alpha_{2} = 35.98 ^{\circ} [/tex]
Finally, the angle between the two refracted beams is:
[tex]\alpha_{2}_{(\lambda=700nm)} - \alpha_{2}_{(\lambda =450nm)} = 35.98 ^{\circ} - 35.76 ^{\circ} = 0.22 ^{\circ}[/tex]
I hope it helps you!
